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Antiparallel vectors have direction angles that differ by 180°. Orthogonal vectors have direction angles that differ by 90°. When a vector is multiplied by a scalar, the result is another vector of a different length than the length of the original vector.
- 1.1: Vectors
The trick is to select two (or three, if necessary)...
- 2.3: Scalars and Vectors
Two vectors that have identical directions are said to be...
- 1.1: Vectors
The parallel vectors are vectors that have the same direction or exactly the opposite direction. i.e., for any vector a, the vector itself and its opposite vector -a are vectors that are always parallel to a.
Make the parallel translation of each vector to a point where their origins (marked by the dot) coincide and construct a parallelogram with two sides on the vectors and the other two sides (indicated by dashed lines) parallel to the vectors.
The parallel vectors are vectors that are in the same direction or exactly the opposite direction, which means if we have any vector v, which is one vector, its opposite vector will be -v. Now, these two vectors are always parallel to each other.
The trick is to select two (or three, if necessary) perpendicular axes (they do not have to be horizontal and vertical, they only need to be perpendicular to each other), and break up every vector involved into a sum of two perpendicular vectors parallel to these axes.
12 Ιαν 2024 · Two vectors that have identical directions are said to be parallel vectors—meaning, they are parallel to each other. Two parallel vectors \(\vec{A}\) and \(\vec{B}\) are equal, denoted by \(\vec{A}\) = \(\vec{B}\), if and only if they have equal magnitudes |\(\vec{A}\)| = |\(\vec{B}\)|.
Apply analytical methods of vector algebra to find resultant vectors and to solve vector equations for unknown vectors. Interpret physical situations in terms of vector expressions. Vectors can be added together and multiplied by scalars.